1. in math, the word dilate means to __________________ or ______________ a figure.
2. if a scale factor is less than 1, then your figure gets ____________.
3. if a scale factor is greater than 1, then your figure gets ____________.
4.
graph the dilated image of triangle jkl using a scale factor of 2 and (0,0) as the center of dilation.
j: _______
j: _______
k: _______
k: _______
l: _______
l: _______
5.
graph the dilated image of quadrilateral mnop using a scale factor of 3 and the origin as the center of dilation.
m: _______
m: _______
n: _______
n: _______
o: _______
o: _______
p: _______
p: _______

Question

Accepted Answer

### Question 1
# Brief Explanations:
In mathematics, dilation is a transformation that changes the size of a figure. It can either make the figure larger (enlarge) or smaller (reduce) while maintaining its shape.
# Answer:
enlarge; reduce

### Question 2
# Brief Explanations:
When the scale factor of a dilation is less than 1, the transformation results in a reduction of the figure's size. For example, a scale factor of 0.5 would make the figure half its original size.
# Answer:
smaller (or "reduced")

### Question 3
# Brief Explanations:
A scale factor greater than 1 in a dilation means the figure is being enlarged. For instance, a scale factor of 3 would make the figure three times its original size.
# Answer:
larger (or "enlarged")

### Question 4 (assuming coordinates from the graph, let's estimate the original coordinates first. Let's say from the grid, J is at (2, 4), K at (1, 1), L at (4, 0))
# Explanation:
## Step1: Recall dilation formula
The formula for dilation with center at $(0,0)$ and scale factor $k$ is $(x,y)\to(kx,ky)$.
## Step2: Find $J'$
For $J(2,4)$ and $k = 2$, $J'=(2\times2,4\times2)=(4,8)$.
## Step3: Find $K'$
For $K(1,1)$ and $k = 2$, $K'=(1\times2,1\times2)=(2,2)$.
## Step4: Find $L'$
For $L(4,0)$ and $k = 2$, $L'=(4\times2,0\times2)=(8,0)$.
# Answer:
J: (2, 4); $J'$: (4, 8)
K: (1, 1); $K'$: (2, 2)
L: (4, 0); $L'$: (8, 0)

### Question 5 (assuming original coordinates: M(1, 3), N(3, 2), O(2, -1), P(0, 0))
# Explanation:
## Step1: Dilation formula
With center at origin $(0,0)$ and scale factor $k = 3$, the formula is $(x,y)\to(3x,3y)$.
## Step2: Find $M'$
For $M(1,3)$, $M'=(3\times1,3\times3)=(3,9)$.
## Step3: Find $N'$
For $N(3,2)$, $N'=(3\times3,3\times2)=(9,6)$.
## Step4: Find $O'$
For $O(2,-1)$, $O'=(3\times2,3\times(-1))=(6,-3)$.
## Step5: Find $P'$
For $P(0,0)$, $P'=(3\times0,3\times0)=(0,0)$.
# Answer:
M: (1, 3); $M'$: (3, 9)
N: (3, 2); $N'$: (9, 6)
O: (2, -1); $O'$: (6, -3)
P: (0, 0); $P'$: (0, 0)

(Note: The coordinates for questions 4 and 5 are estimated based on typical grid problems. If the actual coordinates from the graph differ, the dilation should be applied to the correct original coordinates using the same formula $ (x,y) \to (kx,ky) $ with $ k = 2 $ (for question 4) and $ k = 3 $ (for question 5) and center at $(0,0)$.)

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